Show without recourse to any calculating aid that 7^{1/2} + 7^{1/3}
+ 7^{1/4} < 7 and 4^{1/2} + 4^{1/3} + 4^{1/4} > 4 . Sketch
the graph of f(x) = x^{1/2} + x^{1/3} + x^{1/4} -x
Witch of Agnesi
Age 16 to 18 Challenge Level
Sketch the members of the family of graphs given by $$y = {a^3\over
(x^2+a^2)}$$ for $a=1$, $2$ and $3$.